Assertion (A): The tyres of aircrafts are slightly conducting.
Reason (R): If a conductor is connected to ground, the extra charge induced on conductor will flow to ground.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: Aircraft tyres are made slightly conducting to discharge static electricity accumulated during flight.nReason (R) is true: Grounding allows excess charge to flow to Earth.
(R) correctly explains (A) as the purpose of conducting tyres is to discharge static charge to the ground safely.
Assertion (A): Both the charge and mass are invariant.
Reason (R): Charge is always associated with mass.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true, considering 'mass' as rest mass, which is invariant, similar to charge. Reason (R) is true: All charged particles possess mass; a massless particle cannot carry charge.
(R) is not the correct explanation for (A), as invariance of charge and rest mass are fundamental properties, not directly explained by their association.
Assertion (A): The electric field due to a charge configuration with total charge zero may not be zero.
Reason (R): Electric field obeys the principle of superposition.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: An electric dipole has zero net charge but produces a non-zero electric field. Reason (R) is true: Electric fields add vectorially due to superposition. (R) correctly explains (A) because individual fields from component charges, even if their sum is zero, combine vectorially to form a net non-zero field.
Assertion (A): Vehicles carrying highly inflammable materials have hanging chains, slightly touching the ground.
Reason (R): The body of a vehicle gets charged when moving through air at high speed.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: These chains are a safety measure to discharge static electricity. Reason (R) is true: Friction between the vehicle's body and air (or tires and road) generates static charge.
(R) correctly explains (A) as the chains provide a path to ground, preventing dangerous sparks from static charge buildup.
Assertion (A): The tyres of aeroplanes are slightly conducting.
Reason (R): During take off and landing of aeroplanes, the friction between tyres and the runway may cause electrification of tyres.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: Conducting tyres prevent hazardous static charge accumulation. Reason (R) is true: Friction during takeoff and landing causes static electrification.
(R) correctly explains (A) because the conducting tyres allow the generated static charge to safely discharge into the runway, preventing sparks and potential ignitions.
Assertion (A): We can shield a charge from electric fields by putting it inside a hollow conductor but we can not shield a body from the gravitational influence of near by matter by putting it inside a hollow sphere.
Reason (R): Gravitational force in between two point mass bodies is independent of the intervening medium them.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: Electrostatic shielding (Faraday cage) works, but gravitational shielding does not. Reason (R) is true: Gravitational force is a fundamental interaction that is unaffected by the medium. (R) correctly explains (A) as electric fields can be screened by charge redistribution in conductors, a mechanism not available for gravity.
Assertion (A): A metal sphere of radius \(1\text{ cm}\) cannot hold a charge of \(1\text{ coulomb}\) in air.
Reason (R): The dielectric strength of air (minimum field required for ionisation of a medium) is \(3\text{ MV/m}\).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: \(1\text{ C}\) is a huge charge for a \(1\text{ cm}\) sphere.
Reason (R) is true: Air's dielectric strength is \(3 \times 10^6\text{ V/m}\). The electric field at the surface \(E = \frac{Q}{4\pi \epsilon_0 R^2}\text{ }\approx 9 \times 10^{13}\text{ V/m}\).
This field greatly exceeds air's dielectric strength, causing electrical breakdown. Thus, (R) explains (A).
Assertion (A): In any electrostatic field, a charge cannot be in stable equilibrium.
Reason (R): An electrostatic field is a conservative force field.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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According to Earnshaw's Theorem, a charge cannot be in stable equilibrium in an electrostatic field, thus Assertion (A) is true. An electrostatic field is a conservative force field, so Reason (R) is true. However, the conservative nature of the field is not the direct explanation for Earnshaw's theorem, which is derived from Gauss's law and the Laplace equation.
Assertion (A): If a proton and an electron are placed in the same uniform electric field one by one, they experience different accelerations (The only force acting on proton and electron is that exerted by uniform electric field).
Reason (R): Electric force on a test charge is independent of its mass.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true because \(a = F/m\). In a uniform electric field \(E\), the magnitude of force on both proton and electron is \(F = eE\). Since their masses are different (\(m_e \neq m_p\)), their accelerations \(a\) will be different. Reason (R) is true as the electric force \(F = qE\) depends on charge \(q\) and electric field \(E\), not mass \(m\). Reason (R) correctly explains Assertion (A).
Assertion (A): When a negative charge \(-q\) is released at a distance \(R\) from the centre and along the axis of a uniformly and positively charged fixed ring of radius \(R\), the negative charge does oscillation but not SHM.
Reason (R): The force on negative charge is always towards the centre of the ring but it is not proportional to the displacement from the centre of the ring.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true. The electric force on charge \(-q\) on the axis of a positively charged ring is a restoring force towards the center, causing oscillation. The force is \(F = \frac{kQqx}{(R^2+x^2)^{3/2}}\). This is not linearly proportional to \(x\) (displacement) unless \(x \ll R\), so it's not SHM. Reason (R) is true. The force is attractive (towards center) and indeed not proportional to \(x\). Reason (R) correctly explains Assertion (A).